具有乘法噪声的二维纳维-斯托克斯方程不变度量的唯一性和渐近稳定性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-07-07 DOI:10.3934/dcds.2023102

B. Ferrario, M. Zanella

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引用次数: 0

摘要

我们建立了二维纳维-斯托克斯方程不变度量的唯一性和渐进稳定性，该方程由有界或亚线性或线性增长的乘法噪声驱动。我们研究的是有效椭圆环境，即我们要求协方差算子的范围包含不稳定方向。我们利用了 Glatt Holtz、Mattingly、Richards（2017）和 Kulik、Scheutzow（2018）的广义渐近耦合技术，这些作者将其用于具有加性噪声的随机 Navier Stokes 方程。在此，我们将展示这些方法是如何灵活地处理乘性噪声的。在我们的论证中，预期值中的 Foias Prodi 估计值起着至关重要的作用，它根据乘性噪声的增长条件具有不同的形式（指数衰减或多项式衰减）。

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Uniqueness of the invariant measure and asymptotic stability for the 2D Navier-Stokes equations with multiplicative noise

We establish the uniqueness and the asymptotic stability of the invariant measure for the two dimensional Navier Stokes equations driven by a multiplicative noise which is either bounded or with a sublinear or a linear growth. We work on an effectively elliptic setting, that is we require that the range of the covariance operator contains the unstable directions. We exploit the generalized asymptotic coupling techniques of Glatt Holtz,Mattingly,Richards(2017) and Kulik,Scheutzow(2018), used by these authors for the stochastic Navier Stokes equations with additive noise. Here we show how these methods are flexible enough to deal with multiplicative noise as well. A crucial role in our argument is played by the Foias Prodi estimate in expected valued, which has a different form (exponential or polynomial decay) according to the growth condition of the multiplicative noise.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.